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A prime constellation is a pattern of nearby primes specified by fixed offsets, such as $\{p,p+2\}$ for a twin primes or $\{p,p+2,p+6,p+8\}$ for a prime quadruplet. Some authors reserve the term for especially densely packed admissible patterns, so that convention should be stated.

A finite offset set is admissible if it does not occupy every residue class modulo any prime. Otherwise every translated pattern has a member divisible by that prime, obstructing prime values except for small exceptions. For instance, the offsets $0,2,4$ cover all classes modulo three, explaining why three primes in that pattern can only be $3,5,7$. Admissibility is necessary, but does not itself prove infinitely many realizations.